Getting Lost In Statistics

Some journeys are longer than others.

Workflow Steps;

1. Create Git Repository

2. Import & Tidy Data

3. Visualise Data, ggplot

4. Statisical Model

5. Markdown Document

Work will be stored on laptop & github, in the directory structure below;

StatsPrac190521

-Data (data will remain on laptop, not on github)

-Scripts (laptop & github)

-Results (laptop & github)

MulligansFlatInfiltration

Water infiltration measurements taken at Mulligans flat woodland reserve.

Factors;Sites(9),Elements(6),Inifiltration Suctions(3)

Response; Infiltration ml_per_minute, (also have soil bulk density & soil moisture measurements)

After visualisation reconsidered statistical analysis

Block; Infiltration Suction(3)

Factors; Sites(9), Elements(6), Bulk Density, Soil Moisture

Response; Infiltration ml_per_minute

optional caption text

optional caption text

library(tidyverse)
## Warning: package 'tidyverse' was built under R version 3.5.3
## -- Attaching packages ------------------------------------------------------------------------- tidyverse 1.2.1 --
## v ggplot2 3.1.0       v purrr   0.3.1  
## v tibble  2.0.1       v dplyr   0.8.0.1
## v tidyr   0.8.3       v stringr 1.4.0  
## v readr   1.3.1       v forcats 0.4.0
## -- Conflicts ---------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(readxl)
## Warning: package 'readxl' was built under R version 3.5.3
#Import
MFdata <- read_excel("../Data/MulligansFlatInfiltration.xlsx", skip=5)

#Tidy data, restructure, delete or combine columns, change coulmn structure to factors,
MFdata1 <-  MFdata[-c(2,4)]
names(MFdata1) <- c("Site_ID", "Element",   "Date", "Bulk_Density_1",   "BD1_percent_moisture", "Bulk_Density_2",   "BD2_percent_moisture", "Average_Bulk_Density", "Infiltration_Rate_potential_minus4cm", "Infiltration_Rate_potential_minus1cm", "Infiltration_Rate_potential_plus1cm")
#str(MFdata1)
MFdata1 <- mutate_at(MFdata1, vars("Site_ID", "Element"), as.factor)
#str(MFdata1)
MFdata1$Average_moisture_percent <- ((MFdata1$BD1_percent_moisture + MFdata1$BD2_percent_moisture)/2)
MFdata2 <-  MFdata1[-c(3,4,5,6,7)] #average BD & infiltration
MFdata2a <- gather(MFdata2, key=Infiltration, value = ml_per_minute, c(4,5,6))
MFdata2a$Infiltration <- factor(MFdata2a$Infiltration, levels = c("Infiltration_Rate_potential_plus1cm", "Infiltration_Rate_potential_minus1cm","Infiltration_Rate_potential_minus4cm"))
MFdata2a$ml_per_minute <- replace(MFdata2a$ml_per_minute, MFdata2a$ml_per_minute == 0.00 , 0.000001) #Need to remove zero before log
MFdata2a$log_ml_per_minute <- log(MFdata2a$ml_per_minute)#log infiltration ml_per_minute
str(MFdata2a)
## Classes 'tbl_df', 'tbl' and 'data.frame':    108 obs. of  7 variables:
##  $ Site_ID                 : Factor w/ 9 levels "MF11-2-B","MF19A-2B",..: 7 7 7 7 7 8 8 8 4 4 ...
##  $ Element                 : Factor w/ 6 levels "Clump Bot","Clump Top",..: 6 5 4 1 2 6 5 4 6 5 ...
##  $ Average_Bulk_Density    : num  0.895 1.064 0.861 0.809 0.683 ...
##  $ Average_moisture_percent: num  32.5 25.8 30.9 32.6 31.1 ...
##  $ Infiltration            : Factor w/ 3 levels "Infiltration_Rate_potential_plus1cm",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ ml_per_minute           : num  0.647143 0.464615 0.536889 0.000001 0.0604 ...
##  $ log_ml_per_minute       : num  -0.435 -0.767 -0.622 -13.816 -2.807 ...
MFdata3 <-  MFdata1[-c(3,8)]
MFdata4 <- gather(MFdata3, key=Bulk_Density, value = grams_per_cubic_cm, c(3,5))
MFdata5 <- gather(MFdata4, key=BD_moisture, value = moisture_percent, c(3,4)) #BD, BDmoisture, & infiltration
MFdata6 <- gather(MFdata5, key=Infiltration, value = ml_per_minute, c(3,4,5)) #tidy but not useful for infiltration
#str(MFdata6)
MFdata6$Infiltration <- factor(MFdata6$Infiltration, levels = c("Infiltration_Rate_potential_plus1cm", "Infiltration_Rate_potential_minus1cm","Infiltration_Rate_potential_minus4cm"))
MFdata6$ml_per_minute <- replace(MFdata6$ml_per_minute, MFdata6$ml_per_minute == 0.00 , 0.000001) #Need to remove zero before log
MFdata6$log_ml_per_minute <- log(MFdata6$ml_per_minute)#log infiltration ml_per_minute
str(MFdata6)
## Classes 'tbl_df', 'tbl' and 'data.frame':    432 obs. of  10 variables:
##  $ Site_ID                 : Factor w/ 9 levels "MF11-2-B","MF19A-2B",..: 7 7 7 7 7 8 8 8 4 4 ...
##  $ Element                 : Factor w/ 6 levels "Clump Bot","Clump Top",..: 6 5 4 1 2 6 5 4 6 5 ...
##  $ Average_moisture_percent: num  32.5 25.8 30.9 32.6 31.1 ...
##  $ Bulk_Density            : chr  "Bulk_Density_1" "Bulk_Density_1" "Bulk_Density_1" "Bulk_Density_1" ...
##  $ grams_per_cubic_cm      : num  0.982 1.141 0.924 0.921 0.722 ...
##  $ BD_moisture             : chr  "BD1_percent_moisture" "BD1_percent_moisture" "BD1_percent_moisture" "BD1_percent_moisture" ...
##  $ moisture_percent        : num  27.3 25.3 29.4 31.6 32.7 ...
##  $ Infiltration            : Factor w/ 3 levels "Infiltration_Rate_potential_plus1cm",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ ml_per_minute           : num  0.647143 0.464615 0.536889 0.000001 0.0604 ...
##  $ log_ml_per_minute       : num  -0.435 -0.767 -0.622 -13.816 -2.807 ...

What to plot, this is where the journey was long & windy.

The need for infiltration suction as a block, scaterplot shows no obvious trend.

###Could be a variation between sites, Bulk Density & Moisture percentage

Also logged infiltration rate (ml/min), after looking at residual plot from statistics

Tried some geom_smooth, but no straight lines, random

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Hypothesis for statistcs; Infiltration Suction trested as a block.

Infiltration Rate (ml/min) affected by Bulk Density & moisture %

Which should be seen in Site_ID, & possibly Element.

Needed to Log(ml/min)

#model data


library(lmerTest)
## Warning: package 'lmerTest' was built under R version 3.5.3
## Loading required package: lme4
## Warning: package 'lme4' was built under R version 3.5.3
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following object is masked from 'package:tidyr':
## 
##     expand
## 
## Attaching package: 'lmerTest'
## The following object is masked from 'package:lme4':
## 
##     lmer
## The following object is masked from 'package:stats':
## 
##     step
MFlm1 <- lmer(ml_per_minute~Element + (1|Infiltration), data = MFdata2a)
anova(MFlm1)
## Type III Analysis of Variance Table with Satterthwaite's method
##         Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Element  13307  2661.4     5   100  1.8424 0.1114
summary(MFlm1)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ml_per_minute ~ Element + (1 | Infiltration)
##    Data: MFdata2a
## 
## REML criterion at convergence: 1054.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6846 -0.6364 -0.2120  0.3322  3.7187 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept)  822     28.67   
##  Residual                 1445     38.01   
## Number of obs: 108, groups:  Infiltration, 3
## 
## Fixed effects:
##                       Estimate Std. Error      df t value Pr(>|t|)
## (Intercept)             22.324     20.845   4.548   1.071    0.338
## ElementClump Top        20.246     17.917 100.000   1.130    0.261
## ElementDispersed Logs   -6.666     17.917 100.000  -0.372    0.711
## ElementOld Log          17.030     14.629 100.000   1.164    0.247
## ElementOpen             -8.070     14.629 100.000  -0.552    0.582
## ElementTree             12.403     14.629 100.000   0.848    0.399
## 
## Correlation of Fixed Effects:
##             (Intr) ElmnCT ElmnDL ElmnOL ElmntO
## ElmntClmpTp -0.430                            
## ElmntDsprsL -0.430  0.500                     
## ElemntOldLg -0.526  0.612  0.612              
## ElementOpen -0.526  0.612  0.612  0.750       
## ElementTree -0.526  0.612  0.612  0.750  0.750
plot(MFlm1)

# no significant diferrence between elements for ml_per_minute

MFlm2 <- lmer(ml_per_minute~Site_ID + (1|Infiltration), data = MFdata2a)
anova(MFlm2)
## Type III Analysis of Variance Table with Satterthwaite's method
##         Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
## Site_ID  27524  3440.5     8    97  2.5624 0.01404 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(MFlm2)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ml_per_minute ~ Site_ID + (1 | Infiltration)
##    Data: MFdata2a
## 
## REML criterion at convergence: 1022.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5845 -0.4719 -0.1169  0.3559  4.0968 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept)  824.8   28.72   
##  Residual                 1342.7   36.64   
## Number of obs: 108, groups:  Infiltration, 3
## 
## Fixed effects:
##                  Estimate Std. Error      df t value Pr(>|t|)   
## (Intercept)        53.599     19.091   3.212   2.808  0.06232 . 
## Site_IDMF19A-2B   -25.183     13.380  97.000  -1.882  0.06282 . 
## Site_IDMF22AZ-4A  -27.758     15.450  97.000  -1.797  0.07551 . 
## Site_IDMF25A-3A   -39.478     14.191  97.000  -2.782  0.00650 **
## Site_IDMF27A-1A   -33.798     15.450  97.000  -2.188  0.03110 * 
## Site_IDMF32/1A     -6.258     14.191  97.000  -0.441  0.66024   
## Site_IDMF34-4B    -15.453     13.380  97.000  -1.155  0.25095   
## Site_IDMF37-1A    -47.041     15.450  97.000  -3.045  0.00300 **
## Site_IDMF38-1A    -45.243     14.191  97.000  -3.188  0.00193 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) S_IDMF1 S_IDMF22 S_IDMF25 S_IDMF27 S_IDMF32 S_IDMF34
## S_IDMF19A-2 -0.350                                                     
## S_IDMF22AZ- -0.303  0.433                                              
## S_IDMF25A-3 -0.330  0.471   0.408                                      
## S_IDMF27A-1 -0.303  0.433   0.375    0.408                             
## S_IDMF32/1A -0.330  0.471   0.408    0.444    0.408                    
## S_IDMF34-4B -0.350  0.500   0.433    0.471    0.433    0.471           
## S_IDMF37-1A -0.303  0.433   0.375    0.408    0.375    0.408    0.433  
## S_IDMF38-1A -0.330  0.471   0.408    0.444    0.408    0.444    0.471  
##             S_IDMF37
## S_IDMF19A-2         
## S_IDMF22AZ-         
## S_IDMF25A-3         
## S_IDMF27A-1         
## S_IDMF32/1A         
## S_IDMF34-4B         
## S_IDMF37-1A         
## S_IDMF38-1A  0.408
plot(MFlm2)

# significant difference between sites, 
#especially at the following Site_ID; MF25A-3A, MF27A-1A, MF37-1A, MF38-1A.
#residual plot shows need for log transformation

MFlm10 <- lmer(log_ml_per_minute~Site_ID + (1|Infiltration), data = MFdata2a)
anova(MFlm10)
## Type III Analysis of Variance Table with Satterthwaite's method
##         Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
## Site_ID 103.39  12.924     8    97  2.5465 0.01459 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(MFlm10)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Site_ID + (1 | Infiltration)
##    Data: MFdata2a
## 
## REML criterion at convergence: 470.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.5386 -0.3716  0.2192  0.5058  1.3507 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept) 3.738    1.934   
##  Residual                 5.075    2.253   
## Number of obs: 108, groups:  Infiltration, 3
## 
## Fixed effects:
##                  Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)        3.6005     1.2588  2.9996   2.860 0.064568 .  
## Site_IDMF19A-2B   -2.0685     0.8226 97.0000  -2.515 0.013563 *  
## Site_IDMF22AZ-4A  -2.1489     0.9499 97.0000  -2.262 0.025911 *  
## Site_IDMF25A-3A   -1.7540     0.8725 97.0000  -2.010 0.047179 *  
## Site_IDMF27A-1A   -2.8437     0.9499 97.0000  -2.994 0.003496 ** 
## Site_IDMF32/1A    -0.6654     0.8725 97.0000  -0.763 0.447504    
## Site_IDMF34-4B    -2.8965     0.8226 97.0000  -3.521 0.000657 ***
## Site_IDMF37-1A    -2.6958     0.9499 97.0000  -2.838 0.005528 ** 
## Site_IDMF38-1A    -2.2412     0.8725 97.0000  -2.569 0.011733 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) S_IDMF1 S_IDMF22 S_IDMF25 S_IDMF27 S_IDMF32 S_IDMF34
## S_IDMF19A-2 -0.327                                                     
## S_IDMF22AZ- -0.283  0.433                                              
## S_IDMF25A-3 -0.308  0.471   0.408                                      
## S_IDMF27A-1 -0.283  0.433   0.375    0.408                             
## S_IDMF32/1A -0.308  0.471   0.408    0.444    0.408                    
## S_IDMF34-4B -0.327  0.500   0.433    0.471    0.433    0.471           
## S_IDMF37-1A -0.283  0.433   0.375    0.408    0.375    0.408    0.433  
## S_IDMF38-1A -0.308  0.471   0.408    0.444    0.408    0.444    0.471  
##             S_IDMF37
## S_IDMF19A-2         
## S_IDMF22AZ-         
## S_IDMF25A-3         
## S_IDMF27A-1         
## S_IDMF32/1A         
## S_IDMF34-4B         
## S_IDMF37-1A         
## S_IDMF38-1A  0.408
plot(MFlm10)

# significant difference between sites, 
#especially at the following Site_ID; MF19A-2B, MF22AZ-4A, MF25A-3A, MF27A-1A, MF34-4B, MF37-1A,MF38-1A. MF25A-3A, MF27A-1A, MF37-1A, MF38-1A.
#log_ml_per_minute_ improved residual 

MFlm11 <- lmer(log_ml_per_minute~Average_Bulk_Density + (1|Infiltration), data = MFdata2a)
anova(MFlm11)
## Type III Analysis of Variance Table with Satterthwaite's method
##                      Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Average_Bulk_Density 2.3087  2.3087     1   104  0.4046 0.5261
summary(MFlm11)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Average_Bulk_Density + (1 | Infiltration)
##    Data: MFdata2a
## 
## REML criterion at convergence: 497.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.6286 -0.3152  0.0965  0.5613  1.4598 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept) 3.721    1.929   
##  Residual                 5.705    2.389   
## Number of obs: 108, groups:  Infiltration, 3
## 
## Fixed effects:
##                      Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)            0.8426     1.8273  12.7221   0.461    0.653
## Average_Bulk_Density   0.7868     1.2369 104.0000   0.636    0.526
## 
## Correlation of Fixed Effects:
##             (Intr)
## Avrg_Blk_Dn -0.783
plot(MFlm11)

# no significant difference between Bulk Density, & Infiltration
# log_ml_per_minute_ improved residual 

MFlm12 <- lmer(log_ml_per_minute~Average_moisture_percent + (1|Infiltration), data = MFdata2a)
anova(MFlm12)
## Type III Analysis of Variance Table with Satterthwaite's method
##                          Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Average_moisture_percent 7.0166  7.0166     1   104  1.2396 0.2681
summary(MFlm12)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Average_moisture_percent + (1 | Infiltration)
##    Data: MFdata2a
## 
## REML criterion at convergence: 504.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.8661 -0.3200  0.1924  0.5224  1.3489 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept) 3.722    1.929   
##  Residual                 5.660    2.379   
## Number of obs: 108, groups:  Infiltration, 3
## 
## Fixed effects:
##                           Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                0.98527    1.32963   3.72847   0.741    0.503
## Average_moisture_percent   0.03041    0.02731 104.00000   1.113    0.268
## 
## Correlation of Fixed Effects:
##             (Intr)
## Avrg_mstr_p -0.518
plot(MFlm12)

# no significant difference between Average_moisture_percent
# log_ml_per_minute_ improved residual 

MFlm13 <- lmer(log_ml_per_minute~moisture_percent*grams_per_cubic_cm + (1|Infiltration), data = MFdata6)
anova(MFlm13)
## Type III Analysis of Variance Table with Satterthwaite's method
##                                     Sum Sq Mean Sq NumDF DenDF F value
## moisture_percent                    34.134  34.134     1   426  6.3720
## grams_per_cubic_cm                  26.285  26.285     1   426  4.9066
## moisture_percent:grams_per_cubic_cm 49.218  49.218     1   426  9.1876
##                                       Pr(>F)   
## moisture_percent                    0.011956 * 
## grams_per_cubic_cm                  0.027282 * 
## moisture_percent:grams_per_cubic_cm 0.002585 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(MFlm13)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ moisture_percent * grams_per_cubic_cm + (1 |  
##     Infiltration)
##    Data: MFdata6
## 
## REML criterion at convergence: 1968.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -6.2406 -0.2960  0.1203  0.5430  1.5597 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept) 3.842    1.960   
##  Residual                 5.357    2.315   
## Number of obs: 432, groups:  Infiltration, 3
## 
## Fixed effects:
##                                      Estimate Std. Error        df t value
## (Intercept)                           5.98013    2.64674  53.76706   2.259
## moisture_percent                     -0.21129    0.08370 426.00000  -2.524
## grams_per_cubic_cm                   -4.34277    1.96054 425.99999  -2.215
## moisture_percent:grams_per_cubic_cm   0.21474    0.07085 426.00000   3.031
##                                     Pr(>|t|)   
## (Intercept)                          0.02793 * 
## moisture_percent                     0.01196 * 
## grams_per_cubic_cm                   0.02728 * 
## moisture_percent:grams_per_cubic_cm  0.00259 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) mstr_p grm___
## mostr_prcnt -0.865              
## grms_pr_cb_ -0.894  0.958       
## mstr_pr:___  0.839 -0.987 -0.952
plot(MFlm13)

# significant difference between moisture_percent, grams_per_cubic_cm, &  moisture_percent*grams_per_cubic_cm

MFlm14 <- lmer(log_ml_per_minute~Average_moisture_percent*Average_Bulk_Density + (1|Infiltration), data = MFdata2a)
anova(MFlm14)
## Type III Analysis of Variance Table with Satterthwaite's method
##                                               Sum Sq Mean Sq NumDF DenDF
## Average_moisture_percent                      13.444  13.444     1   102
## Average_Bulk_Density                          10.451  10.451     1   102
## Average_moisture_percent:Average_Bulk_Density 17.965  17.965     1   102
##                                               F value Pr(>F)  
## Average_moisture_percent                       2.4387 0.1215  
## Average_Bulk_Density                           1.8957 0.1716  
## Average_moisture_percent:Average_Bulk_Density  3.2587 0.0740 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(MFlm14)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## log_ml_per_minute ~ Average_moisture_percent * Average_Bulk_Density +  
##     (1 | Infiltration)
##    Data: MFdata2a
## 
## REML criterion at convergence: 499.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.9764 -0.2726  0.0948  0.5030  1.4587 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept) 3.726    1.930   
##  Residual                 5.513    2.348   
## Number of obs: 108, groups:  Infiltration, 3
## 
## Fixed effects:
##                                               Estimate Std. Error       df
## (Intercept)                                     8.3509     5.8203 102.0585
## Average_moisture_percent                       -0.3185     0.2039 102.0000
## Average_Bulk_Density                           -6.4445     4.6806 102.0000
## Average_moisture_percent:Average_Bulk_Density   0.3116     0.1726 102.0000
##                                               t value Pr(>|t|)  
## (Intercept)                                     1.435    0.154  
## Average_moisture_percent                       -1.562    0.121  
## Average_Bulk_Density                           -1.377    0.172  
## Average_moisture_percent:Average_Bulk_Density   1.805    0.074 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Avrg__ Av_B_D
## Avrg_mstr_p -0.945              
## Avrg_Blk_Dn -0.973  0.965       
## Avr__:A_B_D  0.920 -0.989 -0.958
plot(MFlm14)

# no significant difference between moisture_percent, grams_per_cubic_cm, &  moisture_percent*grams_per_cubic_cm

MFlm15 <- lmer(log_ml_per_minute~Site_ID*Element + (1|Infiltration), data = MFdata6)
## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
anova(MFlm15)
## Missing cells for: Site_IDMF22AZ-4A:ElementClump Bot, Site_IDMF25A-3A:ElementClump Bot, Site_IDMF27A-1A:ElementClump Bot, Site_IDMF32/1A:ElementClump Bot, Site_IDMF37-1A:ElementClump Bot, Site_IDMF38-1A:ElementClump Bot, Site_IDMF22AZ-4A:ElementClump Top, Site_IDMF25A-3A:ElementClump Top, Site_IDMF27A-1A:ElementClump Top, Site_IDMF32/1A:ElementClump Top, Site_IDMF37-1A:ElementClump Top, Site_IDMF38-1A:ElementClump Top, Site_IDMF11-2-B:ElementDispersed Logs, Site_IDMF19A-2B:ElementDispersed Logs, Site_IDMF22AZ-4A:ElementDispersed Logs, Site_IDMF27A-1A:ElementDispersed Logs, Site_IDMF34-4B:ElementDispersed Logs, Site_IDMF37-1A:ElementDispersed Logs.  
## Interpret type III hypotheses with care.
## Type III Analysis of Variance Table with Satterthwaite's method
##                 Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
## Site_ID         469.87  58.733     8   394 15.6514 < 2.2e-16 ***
## Element         124.22  24.845     5   394  6.6207 6.201e-06 ***
## Site_ID:Element 366.41  16.655    22   394  4.4382 4.346e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(MFlm15)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Site_ID * Element + (1 | Infiltration)
##    Data: MFdata6
## 
## REML criterion at convergence: 1747
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.9044 -0.3964 -0.0038  0.4240  2.8978 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept) 3.853    1.963   
##  Residual                 3.753    1.937   
## Number of obs: 432, groups:  Infiltration, 3
## 
## Fixed effects:
##                                        Estimate Std. Error        df
## (Intercept)                             3.33153    1.26379   3.05014
## Site_IDMF19A-2B                        -2.15776    0.79084 394.00000
## Site_IDMF22AZ-4A                       -1.80066    0.79084 394.00000
## Site_IDMF25A-3A                        -1.10312    0.79084 394.00000
## Site_IDMF27A-1A                        -1.23904    0.79084 394.00000
## Site_IDMF32/1A                         -1.66241    0.79084 394.00000
## Site_IDMF34-4B                         -6.18787    0.79084 394.00000
## Site_IDMF37-1A                         -3.45990    0.79084 394.00000
## Site_IDMF38-1A                         -2.79824    0.79084 394.00000
## ElementClump Top                        0.16726    0.79084 394.00000
## ElementDispersed Logs                   1.01908    1.11842 394.00000
## ElementOld Log                          0.74246    0.79084 394.00000
## ElementOpen                            -0.15926    0.79084 394.00000
## ElementTree                             0.59460    0.79084 394.00000
## Site_IDMF19A-2B:ElementClump Top       -0.28419    1.11842 394.00000
## Site_IDMF34-4B:ElementClump Top         2.56717    1.11842 394.00000
## Site_IDMF25A-3A:ElementDispersed Logs  -1.77252    1.11842 394.00000
## Site_IDMF32/1A:ElementDispersed Logs    0.39638    1.11842 394.00000
## Site_IDMF19A-2B:ElementOld Log         -0.07907    1.11842 394.00000
## Site_IDMF22AZ-4A:ElementOld Log        -0.77378    1.11842 394.00000
## Site_IDMF25A-3A:ElementOld Log         -1.64256    1.11842 394.00000
## Site_IDMF27A-1A:ElementOld Log         -4.99035    1.11842 394.00000
## Site_IDMF32/1A:ElementOld Log           1.18253    1.11842 394.00000
## Site_IDMF34-4B:ElementOld Log           4.58430    1.11842 394.00000
## Site_IDMF37-1A:ElementOld Log           1.27044    1.11842 394.00000
## Site_IDMF38-1A:ElementOld Log           0.83449    1.11842 394.00000
## Site_IDMF19A-2B:ElementOpen             1.30830    1.11842 394.00000
## Site_IDMF22AZ-4A:ElementOpen           -0.64158    1.11842 394.00000
## Site_IDMF25A-3A:ElementOpen            -0.30919    1.11842 394.00000
## Site_IDMF27A-1A:ElementOpen            -0.19427    1.11842 394.00000
## Site_IDMF32/1A:ElementOpen              1.28811    1.11842 394.00000
## Site_IDMF34-4B:ElementOpen              5.33559    1.11842 394.00000
## Site_IDMF37-1A:ElementOpen              0.65119    1.11842 394.00000
## Site_IDMF38-1A:ElementOpen              0.27286    1.11842 394.00000
## Site_IDMF19A-2B:ElementTree            -0.49875    1.11842 394.00000
## Site_IDMF34-4B:ElementTree              3.96999    1.11842 394.00000
##                                       t value Pr(>|t|)    
## (Intercept)                             2.636 0.076575 .  
## Site_IDMF19A-2B                        -2.728 0.006649 ** 
## Site_IDMF22AZ-4A                       -2.277 0.023328 *  
## Site_IDMF25A-3A                        -1.395 0.163842    
## Site_IDMF27A-1A                        -1.567 0.117979    
## Site_IDMF32/1A                         -2.102 0.036181 *  
## Site_IDMF34-4B                         -7.824 4.74e-14 ***
## Site_IDMF37-1A                         -4.375 1.56e-05 ***
## Site_IDMF38-1A                         -3.538 0.000451 ***
## ElementClump Top                        0.211 0.832608    
## ElementDispersed Logs                   0.911 0.362760    
## ElementOld Log                          0.939 0.348395    
## ElementOpen                            -0.201 0.840502    
## ElementTree                             0.752 0.452584    
## Site_IDMF19A-2B:ElementClump Top       -0.254 0.799554    
## Site_IDMF34-4B:ElementClump Top         2.295 0.022237 *  
## Site_IDMF25A-3A:ElementDispersed Logs  -1.585 0.113805    
## Site_IDMF32/1A:ElementDispersed Logs    0.354 0.723219    
## Site_IDMF19A-2B:ElementOld Log         -0.071 0.943671    
## Site_IDMF22AZ-4A:ElementOld Log        -0.692 0.489437    
## Site_IDMF25A-3A:ElementOld Log         -1.469 0.142727    
## Site_IDMF27A-1A:ElementOld Log         -4.462 1.06e-05 ***
## Site_IDMF32/1A:ElementOld Log           1.057 0.291011    
## Site_IDMF34-4B:ElementOld Log           4.099 5.04e-05 ***
## Site_IDMF37-1A:ElementOld Log           1.136 0.256680    
## Site_IDMF38-1A:ElementOld Log           0.746 0.456031    
## Site_IDMF19A-2B:ElementOpen             1.170 0.242798    
## Site_IDMF22AZ-4A:ElementOpen           -0.574 0.566533    
## Site_IDMF25A-3A:ElementOpen            -0.276 0.782346    
## Site_IDMF27A-1A:ElementOpen            -0.174 0.862188    
## Site_IDMF32/1A:ElementOpen              1.152 0.250132    
## Site_IDMF34-4B:ElementOpen              4.771 2.59e-06 ***
## Site_IDMF37-1A:ElementOpen              0.582 0.560738    
## Site_IDMF38-1A:ElementOpen              0.244 0.807384    
## Site_IDMF19A-2B:ElementTree            -0.446 0.655887    
## Site_IDMF34-4B:ElementTree              3.550 0.000432 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation matrix not shown by default, as p = 36 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it
## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
plot(MFlm15)

#fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
# significant difference between Site_ID, Element, Site_ID*Element
# especially Site_IDMF19A-2B,Site_IDMF22AZ-4A,Site_IDMF32/1A,Site_IDMF34-4B,Site_IDMF37-1A, Site_IDMF38-1A, Site_IDMF34-4B:ElementClump Top, Site_IDMF27A-1A:ElementOld Log, Site_IDMF34-4B:ElementOld Log, Site_IDMF34-4B:ElementOpen, Site_IDMF34-4B:ElementTree     

MFlm16 <- lmer(log_ml_per_minute~Site_ID*Element + (1|Infiltration), data = MFdata2a)
## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
anova(MFlm16)
## Missing cells for: Site_IDMF22AZ-4A:ElementClump Bot, Site_IDMF25A-3A:ElementClump Bot, Site_IDMF27A-1A:ElementClump Bot, Site_IDMF32/1A:ElementClump Bot, Site_IDMF37-1A:ElementClump Bot, Site_IDMF38-1A:ElementClump Bot, Site_IDMF22AZ-4A:ElementClump Top, Site_IDMF25A-3A:ElementClump Top, Site_IDMF27A-1A:ElementClump Top, Site_IDMF32/1A:ElementClump Top, Site_IDMF37-1A:ElementClump Top, Site_IDMF38-1A:ElementClump Top, Site_IDMF11-2-B:ElementDispersed Logs, Site_IDMF19A-2B:ElementDispersed Logs, Site_IDMF22AZ-4A:ElementDispersed Logs, Site_IDMF27A-1A:ElementDispersed Logs, Site_IDMF34-4B:ElementDispersed Logs, Site_IDMF37-1A:ElementDispersed Logs.  
## Interpret type III hypotheses with care.
## Type III Analysis of Variance Table with Satterthwaite's method
##                  Sum Sq Mean Sq NumDF DenDF F value   Pr(>F)   
## Site_ID         117.467 14.6834     8    70  2.7807 0.009904 **
## Element          31.056  6.2112     5    70  1.1763 0.329608   
## Site_ID:Element  91.602  4.1637    22    70  0.7885 0.728528   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(MFlm16)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log_ml_per_minute ~ Site_ID * Element + (1 | Infiltration)
##    Data: MFdata2a
## 
## REML criterion at convergence: 370.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.1639 -0.3276  0.0022  0.3657  2.4654 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  Infiltration (Intercept) 3.733    1.932   
##  Residual                 5.280    2.298   
## Number of obs: 108, groups:  Infiltration, 3
## 
## Fixed effects:
##                                       Estimate Std. Error       df t value
## (Intercept)                            3.33153    1.73332 10.28127   1.922
## Site_IDMF19A-2B                       -2.15776    1.87624 70.00000  -1.150
## Site_IDMF22AZ-4A                      -1.80066    1.87624 70.00000  -0.960
## Site_IDMF25A-3A                       -1.10312    1.87624 70.00000  -0.588
## Site_IDMF27A-1A                       -1.23904    1.87624 70.00000  -0.660
## Site_IDMF32/1A                        -1.66241    1.87624 70.00000  -0.886
## Site_IDMF34-4B                        -6.18787    1.87624 70.00000  -3.298
## Site_IDMF37-1A                        -3.45990    1.87624 70.00000  -1.844
## Site_IDMF38-1A                        -2.79824    1.87624 70.00000  -1.491
## ElementClump Top                       0.16726    1.87624 70.00000   0.089
## ElementDispersed Logs                  1.01908    2.65341 70.00000   0.384
## ElementOld Log                         0.74246    1.87624 70.00000   0.396
## ElementOpen                           -0.15926    1.87624 70.00000  -0.085
## ElementTree                            0.59460    1.87624 70.00000   0.317
## Site_IDMF19A-2B:ElementClump Top      -0.28419    2.65341 70.00000  -0.107
## Site_IDMF34-4B:ElementClump Top        2.56717    2.65341 70.00000   0.968
## Site_IDMF25A-3A:ElementDispersed Logs -1.77252    2.65341 70.00000  -0.668
## Site_IDMF32/1A:ElementDispersed Logs   0.39638    2.65341 70.00000   0.149
## Site_IDMF19A-2B:ElementOld Log        -0.07907    2.65341 70.00000  -0.030
## Site_IDMF22AZ-4A:ElementOld Log       -0.77378    2.65341 70.00000  -0.292
## Site_IDMF25A-3A:ElementOld Log        -1.64256    2.65341 70.00000  -0.619
## Site_IDMF27A-1A:ElementOld Log        -4.99035    2.65341 70.00000  -1.881
## Site_IDMF32/1A:ElementOld Log          1.18253    2.65341 70.00000   0.446
## Site_IDMF34-4B:ElementOld Log          4.58430    2.65341 70.00000   1.728
## Site_IDMF37-1A:ElementOld Log          1.27044    2.65341 70.00000   0.479
## Site_IDMF38-1A:ElementOld Log          0.83449    2.65341 70.00000   0.314
## Site_IDMF19A-2B:ElementOpen            1.30830    2.65341 70.00000   0.493
## Site_IDMF22AZ-4A:ElementOpen          -0.64158    2.65341 70.00000  -0.242
## Site_IDMF25A-3A:ElementOpen           -0.30919    2.65341 70.00000  -0.117
## Site_IDMF27A-1A:ElementOpen           -0.19427    2.65341 70.00000  -0.073
## Site_IDMF32/1A:ElementOpen             1.28811    2.65341 70.00000   0.485
## Site_IDMF34-4B:ElementOpen             5.33559    2.65341 70.00000   2.011
## Site_IDMF37-1A:ElementOpen             0.65119    2.65341 70.00000   0.245
## Site_IDMF38-1A:ElementOpen             0.27286    2.65341 70.00000   0.103
## Site_IDMF19A-2B:ElementTree           -0.49875    2.65341 70.00000  -0.188
## Site_IDMF34-4B:ElementTree             3.96999    2.65341 70.00000   1.496
##                                       Pr(>|t|)   
## (Intercept)                            0.08273 . 
## Site_IDMF19A-2B                        0.25404   
## Site_IDMF22AZ-4A                       0.34050   
## Site_IDMF25A-3A                        0.55846   
## Site_IDMF27A-1A                        0.51117   
## Site_IDMF32/1A                         0.37863   
## Site_IDMF34-4B                         0.00153 **
## Site_IDMF37-1A                         0.06941 . 
## Site_IDMF38-1A                         0.14035   
## ElementClump Top                       0.92922   
## ElementDispersed Logs                  0.70210   
## ElementOld Log                         0.69352   
## ElementOpen                            0.93260   
## ElementTree                            0.75225   
## Site_IDMF19A-2B:ElementClump Top       0.91501   
## Site_IDMF34-4B:ElementClump Top        0.33662   
## Site_IDMF25A-3A:ElementDispersed Logs  0.50632   
## Site_IDMF32/1A:ElementDispersed Logs   0.88168   
## Site_IDMF19A-2B:ElementOld Log         0.97631   
## Site_IDMF22AZ-4A:ElementOld Log        0.77144   
## Site_IDMF25A-3A:ElementOld Log         0.53790   
## Site_IDMF27A-1A:ElementOld Log         0.06417 . 
## Site_IDMF32/1A:ElementOld Log          0.65721   
## Site_IDMF34-4B:ElementOld Log          0.08845 . 
## Site_IDMF37-1A:ElementOld Log          0.63358   
## Site_IDMF38-1A:ElementOld Log          0.75408   
## Site_IDMF19A-2B:ElementOpen            0.62351   
## Site_IDMF22AZ-4A:ElementOpen           0.80965   
## Site_IDMF25A-3A:ElementOpen            0.90757   
## Site_IDMF27A-1A:ElementOpen            0.94184   
## Site_IDMF32/1A:ElementOpen             0.62887   
## Site_IDMF34-4B:ElementOpen             0.04819 * 
## Site_IDMF37-1A:ElementOpen             0.80685   
## Site_IDMF38-1A:ElementOpen             0.91839   
## Site_IDMF19A-2B:ElementTree            0.85145   
## Site_IDMF34-4B:ElementTree             0.13910   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation matrix not shown by default, as p = 36 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it
## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
plot(MFlm16)

# fixed-effect model matrix is rank deficient so dropping 18 columns / coefficients
# significant difference between Site_ID,
# especially Site_IDMF34-4B, Site_IDMF34-4B:ElementOpen